Relative spread
What does coefficient of variation measure?
Coefficient of variation measures standard deviation relative to the magnitude of the mean. Because the result is expressed as a percentage, it can help compare variability between datasets with different scales.
Formula
Coefficient of variation formula
Coefficient of variationCV = standard deviation ÷ |mean| × 100%
The absolute mean is used so that a dataset with a negative mean still produces a positive relative-spread percentage.
Worked example
Calculate CV for 10, 12, and 14
- Mean: (10 + 12 + 14) ÷ 3 = 12.
- Sample standard deviation = 2.
- CV = 2 ÷ 12 × 100%.
- Coefficient of variation = 16.67%.
Interpretation
How to interpret the result
A lower coefficient of variation means the standard deviation is small relative to the mean. A higher value means the data is more dispersed relative to its average.
The meaning of a low or high value depends on the subject, measurement process, and acceptable experimental variation.
Choosing a method
Sample versus population CV
Sample
Uses n − 1
Use this when the measurements are a sample intended to estimate a larger population.
Population
Uses n
Use this when the dataset includes every observation in the population of interest.
Limitations
When coefficient of variation can mislead
- It is undefined when the mean equals zero.
- It can become extremely large when the mean is close to zero.
- It should not be used blindly for data measured on interval scales with arbitrary zero points.
- It does not replace inspection of anomalies or the full data distribution.
Related analysis
Review absolute and relative spread
Use the Standard Deviation Calculator to inspect absolute spread, and the Mean, Median and Mode Calculator to summarize central tendency.
Questions and answers
Coefficient of variation FAQ
What is the coefficient of variation?
The coefficient of variation is the standard deviation divided by the absolute mean, multiplied by 100 percent. It expresses spread relative to the size of the mean.
What does a lower coefficient of variation mean?
A lower coefficient of variation generally indicates that the values are more consistent relative to their mean.
Should I use sample or population standard deviation?
Use sample standard deviation when the observations represent a sample from a larger population. Use population standard deviation when the dataset represents the complete population being analyzed.
Why is coefficient of variation undefined when the mean is zero?
The formula divides standard deviation by the mean. Division by zero is undefined, so coefficient of variation cannot be calculated when the mean is zero.